Protecting personal privacy in a video monitoring system

ABSTRACT

An image acquisition device compresses a media signal representative of a scene based on a sensing matrix that is a determined by a sensing matrix template and a set of template parameters. The image acquisition device provides the compressed media signal to a receiver and selectively provides a specification of a subset of the set of template parameters to the receiver. The receiver extracts one or more scene descriptors representative of one or more portions of the scene from the compressed media signal using the sensing matrix template without knowledge of the template parameters that are not included in the subset. The template parameters that are not included in the subset are not received by the receiver.

BACKGROUND Description of the Related Art

Networks of surveillance cameras have been installed to monitor peopleand objects in public and private places. The images collected by thesurveillance cameras serve a wide array of purposes, including ensuringthe safety and security of the people in these spaces, getting immediateinformation about congestion and occupancy of various facilities,determining when maintenance is necessary, and the like. Many peoplefeel that surveillance cameras are an unwelcome invasion of theirpersonal privacy. People under surveillance may object to being capturedon video by the surveillance cameras and may be uncomfortable with theawareness that video images of them are in the possession of unknownpeople. For example, many people object to being filmed while relaxingat swimming pools or when they are patients in a hospital, particularlywhen there is nothing improper in their behavior.

One approach to balancing the benefits of monitoring public or privatespaces using surveillance cameras and respecting the privacy of thepeople in those spaces is to discard the video images after extractinginformation characterizing the spaces from the video images. However,hackers may still be able to steal the full video images before thevideo images are discarded. Furthermore, the public interest in the fullvideo images can override privacy concerns in some situations, e.g., inthe case of emergencies or if there is a legal obligation to provide thevideo image. Privacy concerns can also be addressed by posting signagethat indicates that an area is under surveillance (which frequentlyincreases visitors' awareness of surveillance and consequently increasestheir discomfort), storing the video images in (hopefully) securedatabases, or simply turning off the surveillance cameras when requested(which may create a security vulnerability).

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is better understood, and its numerous featuresand advantages made apparent to those skilled in the art by referencingthe accompanying drawings. The use of the same reference symbols indifferent drawings indicates similar or identical items.

FIG. 1 is a diagram of a first example of an image acquisition systemaccording to some embodiments.

FIG. 2 is a diagram of a second example of an image acquisition systemaccording to some embodiments.

FIG. 3 is a flow diagram of a method for selectively transmitting arandom number seed from an image acquisition device to a receiveraccording to some embodiments.

FIG. 4 is a diagram of a third example of an image acquisition systemaccording to some embodiments.

FIG. 5 is a flow diagram of a method for acquiring a compressed videosignal using compressive sensing and providing the compressed videosignal to a receiver according to some embodiments.

FIG. 6 is a flow diagram of a method for selectively transmitting randomnumber seeds from a secure server to a receiver according to someembodiments.

FIG. 7 is a flow diagram of a method for selectively receiving randomnumber seeds and reconstructing a video signal from a compressed videosignal according to some embodiments.

DETAILED DESCRIPTION

The benefits of video surveillance of public or private spaces can beretained while respecting the privacy of the people in those spaces bycompressing video signals based on a sensing matrix. As used herein, theterm “sensing matrix” refers to a matrix that is defined by a sensingmatrix template and a set of template parameters. The sensing matrixtemplate is a formula or a rule for constructing the sensing matrixaccording to a set of arguments or variables that are determined by theset of template parameters. The sensing matrix template is resolved intoa uniquely defined sensing matrix by setting each of the variables inthe sensing matrix template to a value of a corresponding parameter fromthe set of template parameters. Operations can then be performed on theresolved matrices. Some embodiments of the sensing matrix templaterequire an empty set of parameters to be resolved, and thus theseembodiments of the sensing matrix template are, in fact, fully specifiedsensing matrices. In some embodiments, the sensing matrix is notexplicitly constructed from the sensing matrix template and the set ofparameters. However, in these embodiments, operations are performed(without explicitly generating the sensing matrix) that are functionallyequivalent to operations that are performed using the sensing matrix,for example, computing the product of the sensing matrix and a vector.These operations require having a full specification of the matrix,which is equivalent to knowing both the sensing matrix template and theset of template parameters.

An estimate of the original video signal can be reconstructed from thecompressed video if the sensing matrix is fully specified, i.e. if boththe sensing matrix template and the template parameters are known. Ifthe sensing matrix template is known, but the set of template parametersis not fully known, it is practically impossible to reconstruct anestimate of the original video signal, but it is possible to determinescene descriptors that represent properties of the incoming videosignals, for example, scene descriptors that indicate speeds anddirections of motions of objects in the video signals can be determinedfrom the compressed video signals using the sensing matrix template, butwithout knowledge of the template parameters, e.g., without using orwithout access to the template parameters. These scene descriptorsprovide enough information for the surveillance task to be conductedsuccessfully, but do not provide information that could compromise theprivacy of the people in the video. Thus, privacy of individuals can beprotected while performing surveillance by selectively providing aspecification of the template parameters (such as random numbergenerator seeds) to receivers that are able to extract scene descriptorsbased on the selectively provided specification, but are not able todecompress the compressed video signals based on the selectivelyprovided specification, as discussed herein. The selectively providedspecification can include a subset of the template parameters.

Some embodiments of the set of template parameters are sequences ofpseudo-random numbers that are generated by one or more random numbergenerators. In this case, each sequence of pseudo-random numbers iscompletely specified by a seed of the corresponding number generator andthe template parameters are reduced to a list of random number generatorseeds. For example, if there is one random number generator and oneseed, the set of template parameters is reduced to a single parameter,the random number generator seed, which completely specifies the wholeset of template parameters.

Some embodiments of the sensing matrix template are a product of a firstrandom matrix and a second matrix. The first random matrix is generatedbased on a first matrix template and a first random number generatorseed that produces a sequence of random numbers to fill the first matrixtemplate. The second matrix is a fully specified matrix. The firstrandom matrix and the second matrix are chosen so that scene descriptorsthat represent properties of the incoming video signals can bedetermined from the compressed video signals using the second matrix andknowledge of the first matrix template, but without knowledge of thefirst random number generator seed, e.g., without using or withoutaccess to the first random number generator seed. The incoming videoitself can be reconstructed if, and only if, the random number generatoris known, and therefore the sensing matrix is uniquely determined. Thus,selectively providing a subset of the template parameters includesproviding a subset of the template parameters that does not includeproviding the first random number generator seed.

The video signals can be derived from the compressed video signals usingthe first random matrix and the second matrix. Some embodiments of thesecond matrix are second random matrices that are generated based onsecond random number generator seeds that are not necessarily equal tothe first random number generator seed. Privacy can be insured byproviding the compressed video signals to a receiver without the firstrandom number generator seed. The second matrix should be known to thereceiver. For example, if the second matrix is a second random matrixdefined by a second random number generator seed, the second randomnumber generator seed can be provided to the receiver. The receiver canthen resolve the second matrix and extract the scene descriptors fromthe compressed video signals using the second matrix and knowledge of afirst matrix template used to define the first matrix. Without access tothe first random number generator seed, the receiver is not able togenerate the first matrix and is therefore unable to re-create the videosignal from the compressed video signal. In some cases, such asemergencies or under legal obligation, the first random number generatorseed can be provided to the receiver so that the receiver can generatethe first random matrix from the first random number generator seed. Thereceiver can then recover the video signals from the compressed videosignals using the first random matrix and the second matrix. In someembodiments, the random number generator seeds are provided to thereceiver in an encrypted form and then the encryption keys for theencrypted seeds are selectively provided based on whether or not thereis an anomaly that requires reconstructing the video signals from thecompressed video signal. For example, if an anomaly is detected and thereceiver is required to reconstruct the video signals, the random numbergenerator seeds or encryption keys are selectively provided to thereceiver.

Video surveillance is the most ubiquitous form of surveillance andtherefore poses a significant challenge to balance the demands foraccurate video surveillance while also respecting privacy. However,surveillance using other modalities such as still images, sound,infrared imaging, and the like are also likely to raise similar privacyissues. In the interest of clarity, embodiments of the techniquesdisclosed herein are described in the context of video surveillance.However, some embodiments of the techniques disclosed herein areapplicable to balancing the demands for accurate surveillance andprivacy during surveillance using other signal modalities. Thus, theterm “media signal” is used herein to refer generally to signals thatcan be used for surveillance including video signals, still images,audio signals, infrared imaging, and the like. Furthermore, althoughembodiments of the sensing matrices described herein are defined by asensing matrix template and a parameter set that consists of a singleparameter such as a random number generator seed, some embodiments ofthe sensing matrices are defined using other sensing matrix templates orother sets of parameters. Similarly, embodiments of the scenedescriptors disclosed herein are motion descriptors, other embodimentsutilize other types of scene descriptors, for example, objectdescriptors that represent objects in the video signals.

FIG. 1 is a diagram of a first example of an image acquisition system100 according to some embodiments. The image acquisition system 100includes an image acquisition device 105 that is used to monitor aregion 110. Some embodiments of the image acquisition device 105 includea video camera that is used to capture video images or other mediasignals representative of the region 110, which can be at any locationincluding public places such as a street corner, a plaza, or a swimmingpool and private places such as a conference room, a store, a hospitalroom, and the like. One or more people 111, 112, 113, 114 (collectivelyreferred to herein as “the people 111-114”) are present in the region110. As discussed herein, the people 111-114 in the region 110 that isbeing monitored or surveilled by the image acquisition device 105 mayobject to having their likenesses captured on video by the imageacquisition device 105 and may be uncomfortable with the awareness thatvideo images of them are in the possession of unknown people.

At least in part to respect the privacy of the people 111-114, the imageacquisition device 105 performs compressive sensing of the region 110 onthe basis of a sensing matrix. Some embodiments of the image acquisitiondevice 105 capture pixels of the image as a matrix of numbers or, if theimage acquisition device 105 is configured to capture color images, aplurality of matrices representing a corresponding plurality of colorcomponents. The pixels of the image are organized as a pixel vector(i.e. a one-dimensional array or a finite sequence of numbers),typically by ordering the pixels in the matrix column by column. Thepixel vector is multiplied by the sensing matrix to produce ameasurements vector, which is typically of a much lower dimension thanthe pixel vector. The measurements vector is then transmitted to thereceiver 115. For example, the measurements vector can be transmittedfrom the image acquisition device 105 to the receiver 115 over a network120. In other embodiments, such as when the image acquisition device 105implements a lensless camera, the light arriving at the imageacquisition device 105 is manipulated to produce an optical signal thatis sampled to produce a measurements vector. In this case, the operationof multiplying the pixel vector by a sensing matrix is performed in theelectro-optical domain, and although no pixels are captured explicitly,the operation is functionally equivalent to that of the former, digitalmethod.

As discussed herein, some embodiments of the image acquisition device105 are configured to capture video signals that are representative ofthe region 110. Video signals can be viewed as a sequence of images,each referred to as a frame. Some embodiments of the image acquisitiondevice 105 process each frame separately, by applying a sensing matrixto that frame and producing a measurements vector. In other embodiments,the image acquisition device 105 divides the video into “blocks” and thesensing matrix is applied to each block. As used herein, the term“block” refers to a spatio-temporal region in the video stream. Thepixels of the block are organized as a pixel vector. For example, ablock can be a fixed rectangular region in several consecutive frames,and the pixel vector is constructed by first concatenating the columnsof the region in each frame and then concatenating the resulting vectorsof the frames in the block. As is the case with a single image, once apixel vector is constructed, it is multiplied by the sensing matrix toproduce a measurements vector that is transmitted to the receiver 115,and as is the case with a single image, the operation of multiplying thepixel vector by the sensing matrix can be implemented in the electrooptical domain, without ever generating the pixel vector explicitly.Examples of compressive sensing of video signals are disclosed in U.S.Patent Application Publication No. 20160021390, which is incorporatedherein by reference in its entirety, and U.S. Patent ApplicationPublication No. 20160249065, which is incorporated herein by referencein its entirety.

Some embodiments of the image acquisition device 105 compress anacquired image or video signal representative of the region 110 based ona sensing matrix that is a product of a first random matrix and a secondmatrix. As used herein, the term “random matrix” refers to a matrix thatis defined by a template that depends on a sequence of random variables.The template is resolved into a particular instance of the random matrixby generating values for each of the random variables in the sequence.For example, a random number generator can generate a sequence ofpseudo-random numbers that are used to populate the sequence of randomvariables. Thus, specifying the seed of the random number generatorcompletely determines the random matrix. In some embodiments, thesequence of random variables directly specifies some or all of theentries of the random matrix. However, as discussed herein, otherembodiments of the sequence may be parameters of an operation that isapplied to a known matrix to produce the random matrix. Entities thathave access to the random number generator seed are able to generate therandom matrix and entities that do not have access to the random numberseed are not able to generate the random matrix, even though the entityknows the template for the random matrix.

To generate a sensing matrix, the first random matrix is generated bypopulating a first matrix template with random numbers generated basedon a first random number generator seed. For example, the imageacquisition device 105 can generate the first matrix using a firstrandom number generator seed that is stored in the image acquisitiondevice 105 or provided to the image acquisition device 105 by a secureserver (not shown in FIG. 1). In some embodiments, the second matrix isalso a random matrix that is generated by populating a second matrixtemplate with random numbers generated based on a second random numbergenerator seed. The acquired video signal cannot be reconstructed fromcompressed video signal without knowledge of the first random numbergenerator seed, e.g., without using or without access to the firstrandom number generator seed. Thus, the image acquisition system 100 isable to protect the privacy of the people 111-114 by selectivelydistributing the first random number generator seeds so that theacquired video signal cannot be reconstructed from the compressed videosignal except in anomalous cases such as emergencies or under legalobligation. For example, a subset of template parameters that does notinclude the first random number generator seeds can be selectivelydistributed to protect privacy of the people 111-114.

The image acquisition system 100 also includes one or more receivers 115that are configured to receive the compressed video signal from theimage acquisition device 105. Some embodiments of the receiver 115 areconfigured to extract scene descriptors from the compressed videosignal. Examples of scene descriptors include motion descriptors thatindicate that there is a moving object at a certain location in scene ofthe region 110 captured by the image acquisition device 105. The motiondescriptors can also characterize a velocity and a direction of motionof the object. Screen descriptors can also include object descriptorsthat indicate the presence of specific objects in the scene of theregion 110.

The receiver 115 is able to extract the scene descriptors from thecompressed video signal without reconstructing the original acquiredvideo signal. The following discloses an example of a process forextracting scene descriptors from a compressed video signal. First, anexample of a technique for detecting motion that can be utilized whenthe pixels of the original video are available is discussed to provide areference. Second, some embodiments of techniques for extracting thesame information from the measurements vector, which is contained in thecompressed video signal, are disclosed. Consider a video block of sizeV×H×T that is captured by the image acquisition device 105, where T isthe number of frames in the block, and in each frame the block containsa rectangle of size V×H of pixels, where V and H are the vertical andhorizontal dimensions of the rectangle, respectively. Let X_(v,h,t),0≤t<T, 0≤h<H, 0≤t<T be the pixels in the block X and let x=[x₀, . . . ,x_(N−1)]^(T) be an N-dimensional pixel vector, N=VHT, whose entries arethe pixels of the block, organized column by column and frame by frame:x=[X _(0,0,0) , . . . ,X _(V-1,0,0) , . . . ,X _(0,1,0) , . . . ,X_(V-1,1,0) , . . . ,X _(V-1,H-1,0) , . . . ,X _(0,0,1) , . . . ,X_(V-1,H-1,1) , . . . ,X _(V-1,H-1,T-1)]^(T)   (1)In other words, each three dimensional pixel index (v,h,t), 0≤t<T,0≤h<H, 0≤t<T is mapped to the one dimensional index 0≤n<N of x accordington=v+Vh+VHt  (2)In the interest of clarity, the video signal is assumed to bemonochrome, with pixel values between 0 and 1. Persons of ordinary skillin the art should be able to modify the following discussion to includeprocessing of color video signals. Let

u

_(k) =u mod(k)denote the remainder when dividing u by k. Let

^(n)x denote the signal x circularly shifted by n:

^(n)=[x _(n) ,x _(n+1, . . . ,) x _(N−1,) x ₀ , . . . ,x _(n−1)]^(T)That is, the entries of

^(n)x are defined by

[𝒯^(n)x]_(j) = x_(⟨n + j⟩_(N))If 0≤j<N is an index, we define

^(n)(j)=

n+j

_(N),hence

^(n) x=[x

_(n) ₍₀₎ , . . . ,x

_(n) _((N-1))]^(T)

In a similar way, one can define a 3-dimensional circular shift on theblock X, by shifting along each dimension separately. If the shift is byk,l,m along the vertical, horizontal and temporal dimensions, then theentries of the shifted block are defined by[

^((k,l,m)) X]_(v,h,t) =x

_(k+v)

_(V) _(,)

_(l+h)

_(H) _(,)

_(m+t)

_(T)Considering (2), it is clear that each 3-dimensional circular shift of Xcorresponds to a 1-dimensional shift of the pixel vector x. In otherwords, if a pixel vector is created out of the shifted block

^((k,l,m))X using (1), with the entries of X replaced by entries of

^((k,l,m))X, it will be of the form

^(n)x wheren+Vl+VHm.  (3)If the block contains no motion, each frame is similar to the onepreceding it, hence

^((0,0,1))X is similar to X. On the other hand, if there is motion inthe block, the moving objects at each frame appear at differentposition, and their speed can therefore be measured in units of pixelsper frame. If the block contains moving objects at a speed of k pixelsvertically and l pixels horizontally, then each frame in the block issimilar to the next frame shifted by k and l pixels vertically andhorizontally, respectively, hence

^((k,l,1))X is similar to X. The issues of wrap-around can be handled byzero-padding and windowing, as explained in more detail in US PatentApplication Publication No. 2015/0178944, which is incorporated hereinby reference in its entirety. Therefore, if X is available, a motion inthe block can be detected and its speed and directions can bedetermined, using the following steps:

-   -   A. For each pair (k,l) which corresponds to feasible motion,        compute the similarity of        ^((k,l,1))X and X.    -   B. Let (k*,l*) be the pair at which the similarity is maximal.        If the similarity for this pair exceeds some threshold, conclude        that there is motion in the video, and its speed components are        k* and l* pixels per frame in the vertical and horizontal        directions, respectively.

Since Eq. (3) establishes a one-to-one correspondence between the3-dimensional shifts on the block X and 1-dimensional shifts on thepixel vector x, these steps could be performed on the pixel vectors,rather than on the pixel blocks. To be more concrete, let

be the set of all shifts n of x that correspond to possible motions,that is, motions that are deemed feasible, in terms of direction andspeed, in the scene of the region 110 being monitored by the imageacquisition device 105. Letu=

(x)  (4)be a vector of features extracted from the pixel vector using a featureextraction operator

. Similarly letu ^((n))=

(

^(n) x)  (5)be the corresponding feature vector extracted from the shifted vector

^(n)x. Let dist(u^((n)),u) be a measure of the distance between u andu^((n)). Then the steps above are equivalently done by finding

$\begin{matrix}{n^{*} = {{\arg\;{\min_{n}{{dist}\left( {u^{(n\;)},u} \right)}}} = {\arg\;{\min_{n}{{dist}\left( {{\left( {\mathcal{T}^{n}x} \right)},{(x)}} \right)}}}}} & (6) \\{d^{*} = {{{dist}\left( {u^{(n^{*})},u} \right)} = {{dist}\left( {{\left( {\mathcal{T}^{n^{*}}x} \right)},{(x)}} \right)}}} & (7)\end{matrix}$and, if d* is less than a threshold, convert the 1-dimension shift n*into a 3-dimension shift on the block, (k*,l*,m*) and conclude thatthere is motion in the block, and its vertical and horizontal componentsare k*/m*, l*/m* pixel per frame, respectively.

A measurements vector is given byy=Φx  (8)where Φ is a M×N matrix that is referred to as the sensing matrix and yis the M-dimensional measurements vector, where MSN and usually M

N. For a well-designed sensing matrix, compressive sensing theoryprovides methods to estimate x given y and Φ. However, while obtainingthe measurements vector according to (8) is a low complexity operation,the reconstruction of an estimate of the original signal given y and tcan be quite complex, but in principle, if y and t had been known, thereceiver 115 could reconstruct x and then use Eqs. (6) and (7) todetermine if there is any motion in the block, and if there is,calculate its velocity components. However, this approach is notpossible if t is not fully known to the receiver 115, as is the case inthe embodiments which we consider now. In these embodiments, thereceiver 115 substitutes u, u^((n)), n∈

by the vectors û, û^((n)), n∈

, respectively, which are extracted from the measurements vector,û=

(y)  (9)û ^((n))=

^(n)(y)  (10)using the feature extraction operators

,

^((n)), n∈

, and a corresponding distance function

ist(û^((n)),û). The vectors û, û^((n)), n∈

and the distance list satisfy the condition:

ist(û ^((n)) ,û)≈dist(u ^((n)) ,u)n∈

  (11)In some embodiments, the vectors û, û^((n)) are estimates of u, u^((n)),n∈

, respectively, but they do not have to be. In fact they do not evenhave to be of the same dimension. All that is necessary is anapproximation of the distances, as shown in (11). The receiver 115replaces equations (6), (7) by{circumflex over (n)}*=arg min_(n∈)

ist(û ^((n)) ,û)=arg min_(n∈)

ist(

^(n)(y),

(y))  (12){circumflex over (d)}*=

ist(û ^((n*)) ,û)=min_(n∈)

ist(

^(n)(y),

(y))  (13)and estimates the motion using {circumflex over (n)}*, {circumflex over(d)}* instead of n*, d*, respectively. Having the approximate operators

,

^(n) is key for this processing. Such an operator does not exist ingeneral, but it exists for specific types of sensing matrices.Computation of motion descriptors is described in further detail in U.S.Patent Application Publication No. 2015/0178944, which is incorporatedherein by reference in its entirety, and U.S. Patent ApplicationPublication No. 2015/0178945, which is incorporated herein by referencein its entirety.

As discussed herein, the first random matrix and the second matrix areconstructed so that the receiver 115 can extract motion descriptors fromthe compressed video signal without knowledge of the first random numbergenerator seed that is used to populate the entries in the first randommatrix. However, the receiver 115 is not able to reconstruct the videosignal from the compressed video signal unless the receiver 115 hascomplete knowledge of both the first random matrix and the secondmatrix, e.g., using the first random number generator seed. Thus,privacy of the people 111-114 can be insured by not providing the firstrandom number generator seed to the receiver 115, except in the case ofanomalous events such as emergencies or under legal obligation.

Some embodiments of the sensing matrix Φ are defined as:Φ=ΓΦ  (14)where Θ is the first random matrix and Γ is the second matrix. Thisconfiguration allows monitoring while preserving privacy. The receiver115 has enough information to generate motion scene descriptors that arenecessary for performing the monitoring task. However, the receiver 115cannot reconstruct the original video signal, which would violate theprivacy of the monitored area and monitored people 111-114. If, however,an anomaly happens, it may be decided that under the circumstances it isjustified to violate the privacy concerns of the people 111-114 in orderto get more information. In that case, all that is needed is to providethe receiver 115 with the random number seed for Θ, which gives it thecomplete definition of Φ and thus allows it to reconstruct the videosignal from the compressed video signal. Some embodiments of thereceiver 115 are able to extract scene descriptors, such as motiondescriptors, from the compressed video signal without knowledge of thefirst random number generator seed.

In the embodiments described below, Γ and ↓ are of sizes M×N and N×N,respectively. Θ is a random transform matrix, hence z, defined by (15)is a random vector of transform coefficients. The second matrix Γ is aselection matrix, which is defined herein to mean that all but one ofthe entries in each row and each column of F have a value of zero andonly one entry in each row has a value of one. Let s (i) be the index ofthe non-zero entry in the ith row, i=0, . . . , M−1. Theny=Γz=[z _(s(0)) , . . . ,z _(s(m-1))]^(T).  (16)

In other words, the measurements vector is obtained by applying therandom transform Θ to the video signal and then selecting the subset ofthe transform coefficients which corresponds to indices s(0), . . . ,s(M−1) using the selection matrix Γ. In the illustrated embodiments, theindices s(0), . . . , s(M−1) are distinct.

In these embodiments, shifts

^(n) in the signal domain can be mapped into corresponding shifts in themeasurement domain. For 0≤i<N letS _(n)(i)={

^(n)(i)|n∈

}be the set of all feasible shifts of i. If

⊆{0, . . . , N−1} is a set of indices we define

(

)={i∈

|

(i)⊆

}  (17)as the set of all indices in

such that all their feasible shifts are also in

. Let

={s(0), . . . ,s(M−1)}  (18)

′=

(

)⊆

  (19)M′=|

|  (20)where |

| denotes the number or members in

. Let s′(0), . . . , s′(M−1) be the subsequence of s(0), . . . , s(M−1)consisting of the indices which are in

′ and definey′=[z _(s′(0)) , . . . ,z _(s′(M′-1))]^(T)  (21)

^(n)(y′)=[z

_(n) _((s′(0))) , . . . ,z

_(n) _((s′(M′-1)))]^(T) , n∈

  (22)

Algorithm 1: Choosing s(0), . . . , s(M − 1) using a greedy algorithm 1.Receive M, N and

 as arguments 2. Initialize

 = ϕ (the empty set) 3. While | 

 | < M  3.1. Let

 ′ =

 ( 

 ). We try to add indices into M so that some    of the indices in

 −

 ′ will move into

 ′. Let C be the    set of all indices in

 −

 ′ for which this is possible:     C = {c ∈

 | 

 (c)

 

 , M ≥ | 

 ∪

 (k)|}.  3.2. If C is empty:    3.2.1. Choose one index k, at random,from {0, . . . , N − 1} −  

   3.2.2. Set

 :=

  ∪ {k}  3.3. Else    3.3.1.${{Let}\mspace{14mu} c_{\max}} = {\arg\mspace{11mu}{\max_{c \in C}{\frac{{\mathcal{J}_{\mathcal{N}}\left( {\mathcal{M}\bigcup{S_{\mathcal{N}}(c)}} \right)}}{{\mathcal{M}\bigcup{S_{\mathcal{N}}(c)}}}.}}}$   3.3.2. Set

 :=

  ∪

 (c_(max)) 4. Let s(0), . . . , s(M − 1) be the members of  

 , sorted in increasing  order.

By definition, the entries of y′ and of

^(n)(y′), n∈

are subsets of the entries of y, hence y′ and

^(n)(y′), n∈

can be computed by the receiver 115, without full knowledge of the firstrandom matrix Θ.

The embodiments mentioned above, in which shifts

^(n) in the signal domain can be mapped into corresponding shifts in themeasurement domain, typically do not use all the measurements but onlythe measurements in y′ defined in Eq. (21), that is only the transformcoefficients whose values are in

′ defined in Eq. (19). The effectiveness of the algorithms describedbelow is improved as M′ gets larger. If s(0), . . . , s(M−1) areselected completely at random, M′ can be quite small or even zero.Therefore, in some embodiments the indices s(0), . . . , s(M−1) arechosen to increase M′, preferably to a relatively large value. Thealgorithm below achieves this.

Some of the embodiments described below use the Discrete FourierTransform (DFT). In the description below the DFT matrix F is definedas:F=[f _(k,l)]_(0≤k,l<N) ,f _(k,l) =N ^(−1/2) exp(2πikl/N)  (23)Hence F is unitary—F⁻¹=F*. In addition, it is assumed that the values ofN are even numbers. However, it should be clear to a person skilled inthe art that other embodiments can be implemented with differentdefinitions of the DFT or with odd values of N.

A first embodiment of the first random matrix is defined based on arandom circulant transform. For example, the first random matrix can bedefined as:

$\begin{matrix}{\Theta = \begin{bmatrix}{w(0)} & {w\left( {N - 1} \right)} & \ldots & {w(1)} \\{w(1)} & {w(0)} & \ldots & {w(2)} \\\vdots & \vdots & \ddots & \vdots \\{w\left( {N - 1} \right)} & {w\left( {N - 1} \right)} & \ldots & {w(0)}\end{bmatrix}} & (24)\end{matrix}$where w(0), . . . w(N−1) is a sequence of independent,identically-distributed (IID), zero mean, random variables, or asequence of pseudo-random numbers with the same properties. The receiver115 can determine motion descriptors from the measurements vector, asdiscussed in U.S. Patent Application Publication No. 2015/0178945, whichis incorporated herein by reference in its entirety. The methoddescribed in that patent application does not require knowledge of thevalues of w(0), . . . , w(N−1). Therefore, this operation can be doneeven when the receiver 115 does not know these values, e.g., because itdoes not know the first random number generator seed used to generatethe values. More specifically, according to the definition of Θ in (24),z=Θx is the convolution of the sequence w(0), . . . w(N−1), extended asa periodic sequence of period N, with the sequence x₀, . . . , x_(N−1).Therefore, Θ

^(n)x=

^(n)Θx=

^(n)z. Using the notation of (21) and (22), let

(x), u, u^((n)), and dist (u^((n)), u) of Eqs. (4)-(7) be defined by

u = (x) = z u^((n)) = (𝒯^(n)x) = 𝒯^(n)(z)${{dist}\left( {u,u^{(n)}} \right)} = {{\frac{1}{\sqrt{N}}{{u^{(n)} - u}}_{2}} = \sqrt{\frac{1}{N}{\sum\limits_{j = 0}^{N - 1}\;\left( {z_{\mathcal{T}^{n}{(j)}} - z_{j}} \right)^{2}}}}$The values of u, u^((n)) are not known to the receiver (even if thematrix t is fully known to it). Hence the following approximationsaccording to (9), (10) can be used:

$\mspace{20mu}{\hat{u} = {{\overset{\sim}{\mathcal{G}}(y)} = y^{\prime}}}$$\mspace{20mu}{{\hat{u}}^{(n)} = {{\overset{\sim}{\mathcal{G}^{n}}(y)} = {{{{\overset{\sim}{\mathcal{T}}}^{n}\left( {y^{\prime},} \right)}n} \in}}}$${{dist}\left( {\hat{u},{\hat{u}}^{(n)}} \right)} = {{\frac{1}{\sqrt{M^{\prime}}}{{{\hat{u}}^{(n)} - \hat{u}}}_{2}} = \sqrt{\frac{1}{M^{\prime}}{\sum\limits_{j \in M^{\prime}}\left( {z_{\mathcal{T}^{n}{({s{(j)}})}} - z_{s{(j)}}} \right)^{2}}}}$Since the entries of y′,

^(n)(y′) are entries of y, they are known to the receiver 115. Note thatdist²(u,u^((n))) is the mean of the sequence of random variables

(z_(𝒯^(n)(j)) − z_(j))²,j=0, . . . , N−1, while

ist²(û,û^((n))) is the mean of a sample of size M′ from that sequence,hence

ist(u,u^((n))) is an approximation to dist (u,u^((n))) and the rest ofthe solution follows as described above using Eqs. (12) and (13).

The solution described above uses the fact that the matrix Θ is of theform (24), which is the first matrix template that can be used togenerate the first random matrix. However, the receiver 115 can performthe solution without knowledge of the values of w(0), . . . , w(N−1)that are used to populate the first matrix template, e.g., without usingor without access to the values. Therefore, motion detection can be donewith only partial knowledge of the sensing matrix. The quality of theapproximation of dist (u^((n)), u) by

ist(û^((n)),{right arrow over (u)}) is improved as M′ is increased. Inorder to get a high value of M′ for the given M,N,

, some embodiments of the selection matrix Γ are determined usingAlgorithm 1.

A second embodiment of the first random matrix is defined based on arandomized discrete Fourier transform. In this embodiment, the pixelsget their values in an interval which is symmetric about zero, that is,|x_(n)|≤P for some constant P. If this is not the case with the originalpixels, they can be translated to satisfy this requirement. Let a randommatrix be defined as:

$\begin{matrix}{R = \begin{bmatrix}r_{0} & 0 & \ldots & 0 \\0 & r_{1} & \; & \vdots \\\vdots & \; & \ddots & 0 \\0 & \ldots & 0 & r_{N - 1}\end{bmatrix}} & (25)\end{matrix}$where R is a diagonal random matrix whose diagonal elements, r₀, . . . ,r_(N−1), are IID random variables which get the values {1, −1} withequal probability (e.g., the random variables are Rademacher randomvariables). Letv=Rx.

The entries of v get their values in the same interval as the entries ofx and they have the same magnitude as the corresponding entries of x,but their signs are toggled randomly. Let V=Fv be the DFT of the randomsignal v. Since v is real, V is conjugate symmetric and is fullydetermined by the N real valuesRe{V ₀ },Re{V ₁ },Im{V ₁ }, . . . ,Re{V _(n/2-1) },Re{V _(n/2-1) },Im{V_(n/2-1)}Letz=[Re{V ₀ },Re{V ₁ },Im{V ₁ }, . . . Re{V _(n/2-1) },Re{V _(n/2-1)},Im{V _(n/2-1)}]^(T)and let G be the real matrix such thatz=Gv.  (26)The first random matrix can then be defined as:Θ=GR.  (27)Note that this definition makes (26) consistent with (15). In thisembodiment, the first random matrix Θ is random because R is random.Therefore, if the key or random number generator seed to R is notsupplied to the receiver 115, the receiver 115 cannot reconstruct thevideo signal from the compressed video signal.

The second matrix Γ is a selection matrix as described above and itsoperation is defined by Eq. (16). Γ is defined so that it selectscomplete DFT coefficients: if the real part of a coefficient isselected, the imaginary part is also selected and vice versa. Morespecifically,s(0)=0

If M is even, s(M−1)=N/2

and if 0<s(i)<M, then

If s(i) is odd and i<M−1: s(i+1)=s(i)+1

If s(i) is even and i>0: s(i−1)=s(i)−1

Therefore, some of the entries of V are immediately available from themeasurements. Let

be the set of indices k for which V_(k) is known from the measurements(including entries derived by the conjugate symmetry V_(k)=V _(N−k)). Itis easy to verify (separating the cases that M is even or odd) that |

|=M+1. Let u be the video signal whose pixel values are the squares ofthe pixel values of the original signal x:u=

(x)=[u ₀ , . . . ,u _(N˜1)]^(T) ,u _(j) =x _(j) ² =v _(j) ²and accordingly let u^((n)) be the u shifted by n:u ^((n))=

^(n)(x)=

(

^(n) x)=

^(n) uThe squaring causes a distortion in the intensity of the video signal,but it does not change the spatial relationships among objects andmotion appears in the signal u in the same way that it appears in theoriginal signal x. Let U=Fu be the Fourier transform of u. Then by thewell-known properties of the DFT:(F

^(n) u)_(k)=exp(−2πink/N)U _(k) ,k=0, . . . ,N−1The L² distance is used to determine a dissimilarity measure, hence theobject of minimization in (6) and (7) becomes:

$\begin{matrix}{{{dist}^{2}\left( {u^{(n)},u} \right)} = {{{u^{(n)} - u}}_{2}^{2} = {{{{\mathcal{T}^{n}u} - u}}_{2}^{2} = {{\sum\limits_{l = 0}^{N - 1}\;{{U_{l}\left( {{\exp\left( {2\;\pi\;{{inl}/N}} \right)} - 1} \right)}}^{2}} = {\sum\limits_{l = 1}^{N - 1}{h_{l}{U_{l}}^{2}}}}}}} & (28) \\{\mspace{85mu}{h_{l} = \left\{ \begin{matrix}{8\;{\sin^{2}\left( {n\; l\;{\pi/N}} \right)}} & {0 < l < {N/2}} \\{4{\sin^{2}\left( {n\;{\pi/2}} \right)}} & {l = {N/2}}\end{matrix} \right.}} & (29)\end{matrix}$

In the video signals produced by monitoring of real scenes, e.g.,monitoring of the region 110 by the camera 105, most of the energy isconcentrated at the low frequencies. Let

⊆{1, . . . , N} be the set of indices which correspond to lowfrequencies (since the signal is 3-dimensional, these indices areusually not consecutive). The DFT of the product of two signals is theconvolution of their DFTs (scaled by N^(−1/2)), therefore:

$\begin{matrix}{U_{l} = {{N^{{- 1}/2}{\sum\limits_{k = 0}^{N - 1}{V_{k}V_{{\langle{l - k}\rangle}_{N}}}}} = {{N^{{- 1}/2}{\sum\limits_{k = 0}^{N - 1}{V_{k}{\overset{\_}{V}}_{{\langle{k - l}\rangle}_{N}}}}} = {{N^{1/2}\left( {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{V_{\mathcal{T}^{(l)}{(k)}}{\overset{\_}{V}}_{k}}}} \right)}.}}}} & (30)\end{matrix}$

Using the definition in equation (17), let

′=

(

). Thus, if k∈

′⊆

then

^(l)(k)∈

for any l∈

. The expression in parenthesis on the right hand side of (30) is themean of the identically distributed random variables

V _(k), 0≤k<N, which can be estimated by the mean of a sample of thoserandom variables:

$\begin{matrix}{{{\hat{U}}_{l} = {{\frac{N^{1/2}}{\mathcal{K}^{\prime}}{\sum\limits_{k \in \mathcal{K}^{\prime}}\;{V_{\mathcal{T}^{(l)}{(k)}}{\overset{\_}{V}}_{k}}}} \approx U_{l}}},\mspace{14mu}{l \in \mathcal{L}}} & (31)\end{matrix}$Substituting these approximations in (28) produces:

$\begin{matrix}{{{u^{(n)} - u}}_{2}^{2} \approx {\sum\limits_{l \in \mathcal{L}}\;{h_{l}{{\hat{U}}_{l}}^{2}}}} & (32)\end{matrix}$where h(l), l∈

are deterministic values defined by (29), and therefore known to thereceiver 115. Let s′(0), . . . , s′(|

|−1) be the indices in

′ in increasing order. Define

$\begin{matrix}{\hat{u} = {{\overset{\sim}{\mathcal{G}}(y)} = \left\lbrack {V_{s^{\prime}{(0)}},\ldots\mspace{14mu},V_{s^{\prime}{({{\mathcal{K}^{\prime}} - 1})}}} \right\rbrack^{T}}} & (33) \\{{\hat{u}}^{(n)} = {{{\overset{\sim}{\mathcal{G}}}^{n}(y)} = \left\lbrack {V_{\mathcal{T}^{n}{({s^{\prime}{(0)}})}},\ldots\mspace{14mu},V_{\mathcal{T}^{n}{({s^{\prime}{({{\mathcal{K}^{\prime}} - 1})}})}}} \right\rbrack^{T}}} & (34)\end{matrix}$By definition, û and û^((n)), n∈

can be derived from y because their entries are composed from entries ofy. By substituting the left hand side of (31) into the right hand sideof (32) one defines:

$\begin{matrix}{{{dist}^{2}\left( {{\hat{u}}^{(n)},\hat{u}} \right)} = {{\frac{N}{{\mathcal{K}^{\prime}}^{2}}{\sum\limits_{l \in \mathcal{L}}\;{h_{l}{{\sum\limits_{k = 0}^{{\mathcal{K}^{\prime}} - 1}\;{V_{\mathcal{T}^{(l)}{({s^{\prime}{(k)}})}}{\overset{\_}{V}}_{s^{\prime}{(k)}}}}}^{2}}}} = {{\frac{N}{{\mathcal{K}^{\prime}}^{2}}{\sum\limits_{l \in \mathcal{L}}\;{h_{l}\left( {{\hat{u}}^{T},{\hat{u}}^{(l)}} \right)}}} \approx {{dist}^{2}\left( {u^{(n)},u} \right)}}}} & (35)\end{matrix}$By using definitions (33)(35) in the minimization problem of equations(9), (10), the receiver 115 can assess if there is motion in the scenerepresented in the compressed video signal, and if there is, a directionand a speed of the motion can be estimated.

In order for the approximation in (31) to work well, the set of indices

′ should be as large as possible. In order to achieve this, someembodiments of the receiver 115 or other entity can select s(0), . . . ,s(M−1), or equivalently, the entries in

, using Algorithm 1, with

taking the role of

. There is a trade-off between the size of

and the size of

′: the larger

is, the better the approximation. However, as

becomes larger

′ becomes smaller, because each additional element in

imposes additional constraints on

′=

(

), and therefore the approximation (31) becomes worse.

It is clear from Eqs. (33)(35) that the receiver can compute

ist(û^((n)),û), and therefore, produce estimated motion descriptors,even if the receiver does not have the random number generator seedwhich allows it to generate the random sequence r₀, . . . , r_(N−1).However, the receiver 115 can reconstruct the video signal from themeasurements if, and only if, it has the random number generator seedwhich allows it to generate r₀, . . . , r_(N−1).

A third embodiment of the first random matrix is defined based on arandom convolution transform. For example, the first random matrix Θ isgiven by:Θ=F ⁻¹ RF  (36)where F is the DFT matrix given by (23) and R is a random diagonalmatrix of the form (25), but with a different definition of the diagonalelements. The diagonal elements r₀, . . . , r_(N−1) here are defined asfollows:

-   -   r₀, . . . , r_(N/2) are independent random variables.    -   r₀ and r_(N/2) get the values {1, −1} with equal probability        (Rademacher random variables).    -   r₁, . . . , r_(N/2-1) are uniformly distributed on the complex        unit circle, that is        r _(k)=exp(iφ _(k)),k=1, . . . ,N/2−1    -   where φ_(k) is uniformly distributed on [0,2π).    -   For N/2<k<N, r_(k)=r _(N−k)

The definition (36) involves complex matrices. Nevertheless, because thesequence r₀, . . . , r_(N−1) is conjugate symmetric, the matrix Θ isreal. Let u=

(x)=x, u^((n))=

^(n)(x)=

^(n)x and define

${{\rho(n)} = {{u^{T}u^{(n)}} = {\sum\limits_{j = 0}^{N - 1}\;{x_{j}x_{{\langle{j + k}\rangle}_{N}}}}}},\mspace{14mu}{0 \leq n \leq {N - 1}}$${{{dist}\left( {u^{(n)},u} \right)} = {{1 - {u}_{2}^{- 2}} = {{u^{T}u^{(n)}} = {1 - \frac{\rho(n)}{\rho(0)}}}}},\mspace{14mu}{n \in}$ρ(n) is the circular autocorrelation of the signal x and the distancedist (u^((n)),u) gets values between zero and one, with low values whenthe correlation coefficient between x and

^(n)x is high, which makes it a reasonable dissimilarity measure.

Let z be defined by (26). It has been shown (in Theorem 2 of R.Haimi-Cohen and Y. M. Lai, “Compressive measurements generated bystructurally random matrices: Asymptotic normality and quantization”,Signal Processing 120, pp. 71-87, 2016, which is incorporated herein byreference in its entirety) that

$\begin{matrix}{{{\rho(n)} = {{NE}\left\{ {z_{j}z_{{\langle{j + n}\rangle}_{N}}} \right\}}},\mspace{14mu}{0 \leq n},{j < N}} & (37)\end{matrix}$Therefore, the value of ρ(n) can be estimated by replacing theexpectation on the right hand side of (37) by averaging several terms ofthe form

z_(j)z_(⟨j + n⟩_(N)).Let

,

″, M′ be defined by (18)-(20) and let s′(0), . . . , s′(M′−1) be thesubsequence of s(0), . . . , s(M−1) consisting of the indices which arein

″. Define

$\begin{matrix}{\hat{u} = {{\overset{\sim}{\mathcal{G}}(y)} = \left\lbrack {z_{s^{\prime}{(0)}},\ldots\mspace{14mu},\; z_{s^{\prime}{({M - 1})}}} \right\rbrack^{T}}} & (38) \\{{{\hat{u}}^{(n)} = {{{\overset{\sim}{\mathcal{G}}}^{n}(y)} = \left\lbrack {z_{\mathcal{T}^{n}{({s^{\prime}{(0)}})}},\ldots\mspace{14mu},z_{\mathcal{T}^{n}{({s^{\prime}{({M - 1})}})}}} \right\rbrack^{T}}},\mspace{14mu}{n \in}} & (39)\end{matrix}$Clearly û, û^((n)), n∈

can be computed from y because by definition, their entries are subsetsof the entries of y, and this computation does not require knowledge ofthe random sequence r₀, . . . , r_(N−1). Then

$\begin{matrix}{{{\rho(0)} \approx {\frac{N}{M^{\prime}}{\sum\limits_{j = 0}^{M^{\prime} - 1}z_{s^{\prime}{(j)}}^{2}}}} = {\frac{N}{M^{\prime}}{\hat{u}}_{2}^{2}}} & (40) \\{{{{\rho(n)} \approx {\frac{N}{M^{\prime}}{\sum\limits_{j = 0}^{M^{\prime} - 1}{z_{s^{\prime}{(j)}}z_{\mathcal{T}^{n}{({s^{\prime}{(j)}})}}}}}} = {\frac{N}{M^{\prime}}{\hat{u}}^{T}{\hat{u}}^{(n)}}},\mspace{20mu}{n \in}} & (41)\end{matrix}$Accordingly, the value of dist (u^((n)),u) can be approximated by:

ist(û ^((n)) ,û)=1−∥û∥ ₂ ⁻²({right arrow over (u)} ^(T) û ^((n)))≈dist(u^((n)) ,u),n∈

.  (42)

By using definitions (38), (39), (42) in the minimization problem ofequations (9), (10), one can assess if there is motion in the compressedvideo signal, and if there is, a direction and a speed of the motion canbe estimated. Clearly, this does not require knowledge of R, hencemotion detection can be performed without complete knowledge of Θ, e.g.,without use of or access to the first random number generator seed usedto populate the first matrix template to generate the first randommatrix. The quality of the approximations (40), (41) is improved as M′is increased. In order to get a high value of M′ for the given M,N,

the selection matrix Γ is constructed using Algorithm 1, which resultsin the selection matrix as in the first embodiment discussed above.

FIG. 2 is a diagram of a second example of an image acquisition system200 according to some embodiments. The image acquisition system 200 isused to implement some embodiments of the image acquisition system 100shown in FIG. 1. The image acquisition system 200 includes an imageacquisition device 205 that is used to acquire and process videosignals, e.g., using a camera 210. The image acquisition device 205performs compressive sensing on the acquired video signals to generatecompressed video signals based on a sensing matrix that is equal to theproduct of a first random matrix and a second matrix. In someembodiments, the first random matrix is a random selection matrix andthe second matrix is a transform matrix, while in other embodiments thefirst random matrix is a random transform matrix and the second matrixis a selection matrix as discussed herein. The first random matrix isgenerated based on a first matrix template and a first random numbergenerator seed.

The image acquisition device 205 includes a processor 215 and a memory220. The processor 215 can be used to execute instructions stored in thememory 220 and to store information in the memory 220 such as theresults of the executed instructions. Some embodiments of the processor215 implement a seed generator (SG) 225 that generates random numbergenerator seeds such as the first random number generator seed that isused to generate the first random matrix. The processor 215 alsoimplements a random number generator (RNG) 230 that receives the randomnumber generator seeds from the seed generator 225 and uses the randomnumber generator seeds to generate corresponding random numbers. Forexample, the random number generator 230 is able to generate a firstsequence of random numbers that is used to populate the first matrixtemplate to form the random transform matrix.

The image acquisition device 205 also includes a transceiver 235 that isconfigured to transmit or receive signals according to wired or wirelesscommunication standards. The transceiver 235 can be implemented as asingle integrated circuit (e.g., using a single ASIC or FPGA) or as asystem-on-a-chip (SOC) that includes different modules for implementingthe functionality of the transceiver 235. The transceiver 235 isconfigured to transmit the compressed video signal 240 to a receiver245. The transceiver 235 is also configured to selectively transmit thefirst random number generator seed 250 to the receiver 245. In normaloperation, the transceiver 235 does not transmit the first random numbergenerator seed 250 to the receiver 245 so that the receiver 245 is notable to generate the first sequence of random numbers to populate thefirst matrix template and form the random transform matrix. Thus, thereceiver 245 is not able to reconstruct the original video signal fromthe compressed video signal 240. In some anomalous situations, such asan emergency or under legal obligation, the transceiver 235 transmit thefirst random number generator seed 250 to the receiver 245 so that thereceiver 245 is able to generate the first sequence of random numbersthat are used to reconstruct the original video signal from thecompressed video signal 240. In some embodiments, the transceiver 235transmits the first random number generator seed 250 in encrypted form.The corresponding encryption keys can then be selectively provided tothe receiver 245 to enable decrypting of the encrypted random numbergenerator seeds 250.

The receiver 245 includes a transceiver 260 that is configured totransmit or receive signals according to wired or wireless communicationstandards. The transceiver 260 can be implemented as a single integratedcircuit (e.g., using a single ASIC or FPGA) or as a system-on-a-chip(SOC) that includes different modules for implementing the functionalityof the transceiver 260. The receiver 245 also includes a processor 265and a memory 270. The processor 265 can be used to execute instructionsstored in the memory 270 and to store information in the memory 270 suchas the results of the executed instructions. Some embodiments of theprocessor 265 are configured to extract scene descriptors from thecompressed video signal 240. The processor 265 is also configured toreconstruct the video signal from the compressed video signal on thebasis of the first random number generator seed 250 under anomalousconditions, as discussed herein. The memory 270 is able to store copies275 of the first random number generator seed 250. As discussed herein,the copies 275 can be stored in encrypted form.

FIG. 3 is a flow diagram of a method 300 for selectively transmitting arandom number generator seed from an image acquisition device to areceiver according to some embodiments. The method 300 is implemented insome embodiments of the image acquisition system 100 shown in FIG. 1 andthe image acquisition system 200 shown in FIG. 2. An image acquisitiondevice (such as a video camera) acquires a video signal and usescompressive sensing to form a compressed video signal on the basis of asensing matrix, as discussed herein. In the illustrated embodiment, thesensing matrix is formed from a first random matrix and a second randommatrix, where the first random matrix is formed using a correspondingfirst matrix templates that is populated on the basis of a correspondingfirst random number generator seed that is generated by the imageacquisition device.

At block 305, the image acquisition device generates first random numbergenerator seed. For example, the image acquisition device can generatethe first random number generator seed using a seed generator such asthe seed generator 225 shown in FIG. 2. At block 310, the imageacquisition device populates first matrix template using the sequence ofrandom numbers that is generated based on the first random numbergenerator seed to form the first random matrix. For example, the imageacquisition device can generate the sequence of random numbers using arandom number generator such as the random number generator 230 shown inFIG. 2.

At block 315, the image acquisition device acquires a compressed videosignal by performing compressive sensing on a video signal on the basisof the sensing matrix. At block 320, the image acquisition devicetransmits the compressed video signal to a receiver. As discussedherein, the receiver is able to extract scene descriptors, such asmotion descriptors or object descriptors, from the compressed videosignal. However, without knowledge of the first random number generatorseed, e.g., without using or without access to the first random numbergenerator seed, the receiver is not able to reconstruct the video signalfrom the compressed video signal.

At decision block 325, an anomaly condition can be detected that wouldrequire the image acquisition device to provide the first random numbergenerator seed to the receiver. For example, the image acquisitiondevice can be required to transmit the first random number generatorseed to the receiver in the event of an emergency or under legalobligation. In some embodiments, the receiver determines, based on theextracted scene descriptors, if there is an anomaly, and in that casethe receiver declares an emergency that causes the image acquisitiondevice to provide the first random number generator seed to thereceiver. Under normal operating conditions the image acquisition devicebypasses the transmission of the first random number generator seed tothe receiver (at block 330). If the image acquisition device determinesthat there is a need for it, the image acquisition device transmits thefirst random number generator seed to the receiver (at block 335). Thus,in the event of an anomaly, the receiver acquires the first randomnumber generator seed, which enables the receiver to reconstruct thevideo signal from the compressed video signal.

FIG. 4 is a diagram of a third example of an image acquisition system400 according to some embodiments. The image acquisition system 400 isused to implement some embodiments of the image acquisition system 100shown in FIG. 1. The image acquisition system 400 includes an imageacquisition device 405 that is used to acquire and process videosignals, e.g., using a camera 410. The image acquisition device 405performs compressive sensing on the acquired video signals to generatecompressed video signals based on a sensing matrix that is equal to theproduct of a first random matrix and a second matrix, as discussedherein. The first random matrix is generated based on a first matrixtemplate and a first random number generator seed.

The image acquisition device 405 includes a processor 415 and a memory420. The processor 415 can be used to execute instructions stored in thememory 420 and to store information in the memory 420 such as theresults of the executed instructions. The memory 420 includes a portion425 that is configured to store random number generator seeds. Theprocessor 415 can therefore access the random number generator seedstored in the portion 425 and generate sequences of random numbers, e.g.using a random number generator (not shown in the interest of clarity).The processor 415 can therefore use the stored random number generatorseeds to generate random matrices, as discussed herein. The imageacquisition device 405 also includes a transceiver 430 that isconfigured to transmit or receive signals according to wired or wirelesscommunication standards. The transceiver 430 can be implemented as asingle integrated circuit (e.g., using a single ASIC or FPGA) or as asystem-on-a-chip (SOC) that includes different modules for implementingthe functionality of the transceiver 430. The transceiver 430 isconfigured to transmit the compressed video signal 433 to a receiver435.

The receiver includes a transceiver 440 that is configured to transmitor receive signals according to wired or wireless communicationstandards. For example, the transceiver 440 can receive the compressedvideo signal 433 from the image acquisition device 405. The transceiver440 can be implemented as a single integrated circuit (e.g., using asingle ASIC or FPGA) or as a system-on-a-chip (SOC) that includesdifferent modules for implementing the functionality of the transceiver440. The receiver 435 also includes a processor 445 and a memory 450.The processor 445 can be used to execute instructions stored in thememory 450 and to store information in the memory 450 such as theresults of the executed instructions. The memory 450 includes a portion455 that is configured to store random number generator seeds. Theprocessor 445 can therefore access the random number generator seedstored in the portion 455 and generate a sequence of random numbers,e.g. using a random number generator (not shown in the interest ofclarity). The processor 445 can therefore extract scene descriptors fromcompressed video signals and, if the processor 445 is able to generatethe first random sequence, it can reconstruct an estimate of theoriginal video signal from the compressed video signal.

The image acquisition system 400 also includes a secure server 460 forgenerating and providing random number generator seeds. The secureserver 460 includes a processor 465 and a memory 470. The processor 465can be used to execute instructions stored in the memory 470 and tostore information in the memory 470 such as the results of the executedinstructions. Some embodiments of the processor 465 implement a seedgenerator (SG) 475 that generates random number generator seeds such asa first random number generator seed 480 that is used to generate thefirst random matrix.

The secure server 460 also includes a transceiver 490 that is configuredto transmit or receive signals according to wired or wirelesscommunication standards. The transceiver 490 can be implemented as asingle integrated circuit (e.g., using a single ASIC or FPGA) or as asystem-on-a-chip (SOC) that includes different modules for implementingthe functionality of the transceiver 490. The transceiver 490 isconfigured to transmit the first random number generator seed 480 to theimage acquisition device 405 so that the image acquisition device 405can generate the sensing matrix needed to perform compressive sensing onthe video signal provided by the camera 410. The transceiver 490 is alsoconfigured selectively transmit the first random number generator seed480 to the receiver 435. Some embodiments of the transceiver 490 areconfigured to transmit the first random number generator seed 480 inencrypted form based on different encryption keys. The transceiver 490can then selectively transmit the encryption keys for the first randomnumber generator seed 480 to the receiver 435, which can use thereceived encryption keys to decrypt the encrypted random numbergenerator seed 480.

In normal operation, the transceiver 490 does not transmit the firstrandom number generator seed 480 to the receiver 435 so that thereceiver 435 is not able to generate the first sequence of randomnumbers to populate the first matrix template and form the randomtransform matrix. Thus, the receiver 435 is not able to reconstruct theoriginal video signal from the compressed video signal 433 provided bythe image acquisition device 405. In some anomalous situations, such asan emergency or under legal obligation, the transceiver 490 transmitsthe first random number generator seed 480 to the receiver 435 so thatthe receiver 435 is able to generate the first sequence of randomnumbers that are used to reconstruct the original video signal from thecompressed video signal 433.

FIG. 5 is a flow diagram of a method 500 for acquiring a compressedvideo signal using compressive sensing and providing the compressedvideo signal to a receiver according to some embodiments. The method 500is implemented in some embodiments of the image acquisition system 100shown in FIG. 1 and the image acquisition system 400 shown in FIG. 4. Animage acquisition device (such as a video camera) acquires a videosignal and uses compressive sensing to form a compressed video signal onthe basis of a sensing matrix, as discussed herein. In the illustratedembodiment, the sensing matrix is formed from a first random matrix anda second matrix, which are formed using corresponding a first matrixtemplate that is populated on the basis of corresponding first randomnumber generator seed that the generated by the image acquisitiondevice. However, as discussed above, the first random number generatorseed may be generated by a secure server and transmitted to the imageacquisition device.

At step 505, the image acquisition device receives first random numbergenerator seed, from a secure server. For example, the image acquisitiondevice can transmit a request to a secure server such as the secureserver 460 shown in FIG. 4 and the secure server can transmit the firstrandom number generator seed to the image acquisition device. At step510, the image acquisition device populates first matrix template usingthe first sequence of random numbers that are generated based on thefirst random number generator seeds to form the first random matrices.The first random matrix and second matrix are then combined to form thesensing matrix. At block 515, the image acquisition device acquires acompressed video signal by performing compressive sensing on a videosignal on the basis of the sensing matrix. At block 520, the imageacquisition device transmits the compressed video signal to a receiver.

FIG. 6 is a flow diagram of a method 600 for selectively transmittingrandom number generator seeds from a secure server to a receiveraccording to some embodiments. The method 600 is implemented in someembodiments of the image compression system 100 shown in FIG. 1 in thesecure server 460 shown in FIG. 4. The secure server includes a randomseed generator such as the random seed generator 475 shown in FIG. 4,which is used to generate first random number generator seeds. The firstrandom number generator seed is used to generate a first random, asdiscussed herein.

At step 605, the secure server transmits the first random numbergenerator seed to an image acquisition device such as the imageacquisition device 105 shown in FIG. 1 and the image acquisition device405 shown in FIG. 4. For example, the secure server can receive arequest for the first random number generator seeds from the imageacquisition device and then provide the first random number generatorseeds to the image acquisition device.

At decision step 610, the secure server determines whether there is ananomaly that requires that a receiver reconstruct the video signal fromthe compressed video signal. As discussed herein, the anomaly can be anemergency or a legal obligation. Under normal operating conditions, noanomaly exists and the first random number generator seed is nottransmitted to the receiver. For example, an image acquisition device ora secure server can bypass (at block 615) transmission of the firstrandom number generator seed to the receiver as long as no anomaly isdetected. If an anomaly exists, the secure server transmits (at block620) the first random number generator seed to the receiver, whichenables the receiver to reconstruct the video signal from the compressedvideo signal.

FIG. 7 is a flow diagram of a method 700 for selectively receivingrandom number generator seeds and reconstructing a video signal from acompressed video signal according to some embodiments. The method 700 isimplemented in some embodiments of the receiver 115 shown in FIG. 1, thereceiver 245 shown in FIG. 2, and the receiver 435 shown in FIG. 4. Animage acquisition device (such as a video camera) acquires a videosignal and uses compressive sensing to form a compressed video signal onthe basis of a sensing matrix, as discussed herein. In the illustratedembodiment, the sensing matrix is formed from a first random matrix,which is formed using corresponding first matrix template that ispopulated on the basis of corresponding first random number generatorseed, that is generated by the image acquisition device or received froma secure server, and a second matrix.

At step 705, the receiver receives the compressed video signal from theimage acquisition device. At step 715, the receiver generates one ormore scene descriptors from the compressed video signal using the secondrandom matrix. For example, as discussed herein, the receiver cangenerate one or more motion descriptors from the compressed video signalusing the second matrix and a knowledge of the structure of the firstrandom matrix. However, the receiver does not need the first randomnumber generator seed to extract the motion descriptors from thecompressed video signal.

At step 720, the receiver determines whether there is an anomaly such asan emergency or a legal obligation that requires reconstruction of thevideo signal from the compressed video signal. In some embodiments, thereceiver uses the motion descriptors generated at block 715 to determinewhether an anomaly exists. For example, the motion descriptors mayindicate unusual, suspicious, or dangerous motion within a region beingmonitored to produce the compressed video signal. Under normalcircumstances, the receiver does not detect an anomaly and so thereceiver does not receive the first random number generator seed fromthe image acquisition device or the secure server (at block 725). If thereceiver detects an anomaly, the method 700 flows to step 730.

At step 730, the receiver receives the first random number generatorseed, e.g., from the image acquisition device or the secure server. Atstep 735, the receiver populates the first matrix template using thefirst random number generator seed to form the first random matrix. Forexample, the receiver can generate a sequence of random numbers topopulate the entries in the first matrix template using the first randomnumber generator seed. At step 740, the receiver reconstructs the videosignal from the compressed video signal using the first random matrix,as discussed herein.

In some embodiments, certain aspects of the techniques described abovemay implemented by one or more processors of a processing systemexecuting software. The software comprises one or more sets ofexecutable instructions stored or otherwise tangibly embodied on anon-transitory computer readable storage medium. The software caninclude the instructions and certain data that, when executed by the oneor more processors, manipulate the one or more processors to perform oneor more aspects of the techniques described above. The non-transitorycomputer readable storage medium can include, for example, a magnetic oroptical disk storage device, solid state storage devices such as Flashmemory, a cache, random access memory (RAM) or other non-volatile memorydevice or devices, and the like. The executable instructions stored onthe non-transitory computer readable storage medium may be in sourcecode, assembly language code, object code, or other instruction formatthat is interpreted or otherwise executable by one or more processors.

A computer readable storage medium may include any storage medium, orcombination of storage media, accessible by a computer system during useto provide instructions and/or data to the computer system. Such storagemedia can include, but is not limited to, optical media (e.g., compactdisc (CD), digital versatile disc (DVD), Blu-Ray disc), magnetic media(e.g., floppy disc, magnetic tape, or magnetic hard drive), volatilememory (e.g., random access memory (RAM) or cache), non-volatile memory(e.g., read-only memory (ROM) or Flash memory), ormicroelectromechanical systems (MEMS)-based storage media. The computerreadable storage medium may be embedded in the computing system (e.g.,system RAM or ROM), fixedly attached to the computing system (e.g., amagnetic hard drive), removably attached to the computing system (e.g.,an optical disc or Universal Serial Bus (USB)-based Flash memory), orcoupled to the computer system via a wired or wireless network (e.g.,network accessible storage (NAS)).

Note that not all of the activities or elements described above in thegeneral description are required, that a portion of a specific activityor device may not be required, and that one or more further activitiesmay be performed, or elements included, in addition to those described.Still further, the order in which activities are listed are notnecessarily the order in which they are performed. Also, the conceptshave been described with reference to specific embodiments. However, oneof ordinary skill in the art appreciates that various modifications andchanges can be made without departing from the scope of the presentdisclosure as set forth in the claims below. Accordingly, thespecification and figures are to be regarded in an illustrative ratherthan a restrictive sense, and all such modifications are intended to beincluded within the scope of the present disclosure.

Benefits, other advantages, and solutions to problems have beendescribed above with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any feature(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeature of any or all the claims. Moreover, the particular embodimentsdisclosed above are illustrative only, as the disclosed subject mattermay be modified and practiced in different but equivalent mannersapparent to those skilled in the art having the benefit of the teachingsherein. No limitations are intended to the details of construction ordesign herein shown, other than as described in the claims below. It istherefore evident that the particular embodiments disclosed above may bealtered or modified and all such variations are considered within thescope of the disclosed subject matter. Accordingly, the protectionsought herein is as set forth in the claims below.

What is claimed is:
 1. A method comprising: compressing, at an imageacquisition device, a media signal representative of a scene based on asensing matrix that is a determined by a sensing matrix template and aset of template parameters; providing, from the image acquisitiondevice, the compressed media signal to a receiver; and selectivelyproviding a specification of a subset of the set of template parametersto the receiver so that the media signal cannot be reconstructed fromthe provided compressed media signal using the provided specification ofthe subset of the set of template parameters.
 2. The method of claim 1,wherein the media signal is a video signal.
 3. The method of claim 1,wherein the sensing matrix template comprises at least one matrixtemplate, and wherein said at least one matrix template is determined byparameters from the set of template parameters.
 4. The method of claim3, wherein the set of template parameters comprises at least one randomnumber generator seed, and wherein selectively providing thespecification comprises selectively providing a subset of the set oftemplate parameters that does not include the random number generatorseed.
 5. The method of claim 3, wherein: the at least one matrixtemplate comprises a first random matrix and a second matrix; the set oftemplate parameters comprises a random number generator seed; the firstrandom matrix is determined by a sequence of parameters generated by arandom number generator using the random number generator seed; and thesensing matrix is the product of the first random matrix and the secondmatrix.
 6. The method of claim 5, further comprising: determining thefirst random matrix based on at least one of a random circulanttransform, a locally randomized discrete Fourier transform, or a randomconvolution transform.
 7. The method of claim 1, further comprising:providing a first random number seed in addition to the subset of theset of template parameters in response to detection of an anomaly thatrequires reconstruction of the compressed media signal.
 8. The method ofclaim 1, wherein a specification of the set of template parameters isprovided in response to detecting an anomaly that indicates that thereceiver is required to reconstruct the media signal from the compressedmedia signal.
 9. A method comprising: compressing, at an imageacquisition device, a media signal representative of a scene based on asensing matrix that is a determined by a sensing matrix template and aset of template parameters that includes a random number seed;providing, from the image acquisition device, the compressed mediasignal to a receiver; and selectively providing a specification of asubset of the set of template parameters to the receiver, wherein thesubset does not include the random number seed so that the media signalcannot be reconstructed from the provided compressed media signal usingthe provided specification of the subset of the set of templateparameters.
 10. The method of claim 9, wherein the media signal is avideo signal.
 11. The method of claim 9, wherein the sensing matrixtemplate comprises at least one matrix template, and wherein said atleast one matrix template is determined by parameters from the set oftemplate parameters.
 12. The method of claim 11, wherein: the at leastone matrix template comprises a first random matrix and a second matrix;the set of template parameters comprises a random number generator seed;the first random matrix is determined by a sequence of parametersgenerated by a random number generator using the random number generatorseed; and the sensing matrix is the product of the first random matrixand the second matrix.
 13. The method of claim 12, further comprising:determining the first random matrix based on at least one of a randomcirculant transform, a locally randomized discrete Fourier transform, ora random convolution transform.
 14. The method of claim 13, furthercomprising: providing the random number generator seed to the receiverin response to detection of an anomaly that requires reconstruction ofthe compressed media signal.